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C2×C9×#13133723 #44501638

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C9×#13133723

Splittings

Fitting, HallC2×C9×C11×C31 ⋊ C5
derived, HallC11×C31 ⋊ C2×C5×C9
HallC9×C11×C31 ⋊ C2×C5
HallC2×C11×C31 ⋊ C5×C9
HallC2×C9×C31 ⋊ C11⋊C5
HallC9×C31 ⋊ C2×C11⋊C5
HallC2×C9×C11 ⋊ ΓL(1,𝔽32)
HallC9×C11 ⋊ C2×ΓL(1,𝔽32)
HallC2×C31 ⋊ C9×C11⋊C5
SylowC31 ⋊ C2×C9×C11⋊C5
HallC2×C11 ⋊ C9×ΓL(1,𝔽32)
SylowC11 ⋊ C2×C9×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C9#13133723
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C2×C3×#13133723
FittingC2×C9×C11×C31C5
socleC2×C3×C11×C31C3×C5
prime radicalC2×C3×#13133723C3
cosocleC3×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6138

Conjugacy classes & character table

1314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 5);